Dissertation
Dissertation > Mathematical sciences and chemical > Mathematics > Mathematical Analysis > Differential equations, integral equations

Exact Solutions for Coupled and High-order Nonlinear Schr(?)dinger Equation

Author ZuoZuo
Tutor SunYuHuai
School Sichuan Normal University
Course Computational Mathematics
Keywords Nonlinear partial differential equations (G ’/G)-developing process (G’/G+G’)-developing process The new general algebraic method Improved (G’/G+G’)developing process Symbolic computation Accurate solutions
CLC O175
Type Master's thesis
Year 2013
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Accurate solutions of coupled and high-order nonlinear Schrodingerequations or equitation set are important content in the research of differential equationas well as computer algebra. Currently, it is constructive method that has beencommonly applied in this area. This paper is intended to construct the accurate solutionsfor the coupled equitation set of Schrodinger as well as high order nonlinear equitationof Schrodinger by applying the (G’/G)-developing process,(G’/G+G’)-developing process, a new generalized algebraic method, improved(G’/G+G’)-expansion method and symbol the unity symbol calculation method. These solutions include the periodicwave solutions of triangle function type, singular travelling wave solutions and thehyperbolic function format solutions, etc. These results not only enrich the solutions ofcoupled and high-order nonlinear Schrodinger equations or equitation set,but alsodeepen our understanding applications of nonlinear partial differential equations.

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